Let where
?????? ??????
Guys, i have this problem from Partial Derivatives chapter-Chain Rule. I don't how to get started in this problem. plz guide me.
this is pretty much plugging things into a formula, assuming you knwo how to find partial derivatives.
Note that $\displaystyle W_s = \frac {\partial W}{\partial s} = \frac {\partial F}{\partial s} \underbrace{=}_{\text{chain rule}} \frac {\partial F}{\partial u} \cdot \frac {\partial u}{\partial s} + \frac {\partial F}{\partial v} \cdot \frac {\partial v}{\partial s} $
you want to evaluate these at (1,0)
finding $\displaystyle W_t$ is similar
do you see how to apply the formula in this case? this formula probably wasn't the most efficient way to write it
Note that $\displaystyle W_s(1,0) = \frac {\partial}{\partial s}F(u(1,0),v(1,0))$, now apply the chain rule, similar to how you did in single variable calc ...(differentiate the outside function, multiply by the derivative of the inside, etc, bearing in mind the first formula i gave. note that i used alternative notation. for example, $\displaystyle \frac {\partial F}{\partial u} \cdot \frac {\partial u}{\partial s}$ means $\displaystyle F_u \cdot u_s$)